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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Phase Diagrams of Electric-Fduced Aggregation in Conducting Colloids

Under the application of a sufficiently strong electric field, a suspension may undergo reversible phase transitions from a homogeneous random arrangement of particles into a variety of ordered aggregation patterns. The surprising fact about electric-field driven phase transitions is that the aggregation patterns, that are observed in very diverse systems of colloids, display a number of common structural features and modes of evolution thereby implying that a universal mechanism may exist to account for these phenomena. It is now generally believed that this mechanism emanates from the presence of the long-range anisotropic interactions between colloidal particles due to their polarization in an applied field. But, in spite of numerous applications of the electric-field-driven phenomena in biotechnology, separation, materials engineering, chemical analysis, etc. our understanding of these phenomena is far from complete. Thus, it is the purpose of the proposed research to develop a theory and then test experimentally, under normal- and low-gravity conditions, the accuracy of the theoretical predictions regarding the effect of the synergism of the interparticle electric and hydrodynamic interactions on the phase diagram of a suspension. The main results from our theoretical studies performed to-date enable one to trace how the variations of the electrical properties of the constituent materials influence the topology of the suspension phase diagram and then, by using an appropriate phase diagram, to evaluate how the electric-field-induced transformations will depend on the frequency and the strength of the applied field.

Khusid, B.↗
DOE OSTI2023

Spontaneous Symmetry–Breaking of Nonequilibrium Steady–States Caused by Nonlinear Electrical Transport

Negative differential resistance (NDR) in certain materials has been attributed to spontaneous emergence of symmetry-breaking electrical current density localization from a previously homogeneous distribution, which is postulated to occur due to the nonequilibrium thermodynamic force of minimization of entropy production. However, this phenomenon has not been quantitatively predicted based on intrinsic material properties and an applied electrical stimulus. Herein an instability criterion is derived for localization of current density and temperature from a thermal fluctuation in a parallel conductor model of a thin film that is subject to Newton's law of cooling. The conditions for steady–state electro-thermal localization is predicted, verifying a decrease in entropy production upon localization. Electro-thermal localization accompanied by a decrease of entropy production is confirmed in a multiphysics simulation of current flow in a thin film. The instability criterion predicts conditions for spontaneous current density localization, relating symmetry breaking fundamentally to dynamical instability via Local Activity theory.

36 MATERIALS SCIENCE↗
NASA NTRS2003

Lifetime Predictions of a Titanium Silicate Glass with Machined Flaws

A dynamic fatigue study was performed on a Titanium Silicate glass to assess its susceptibility to delayed failure and to compare the results with those of a previous study. Fracture mechanics techniques were used to analyze the results for the purpose of making lifetime predictions. The material strength and lifetime was seen to increase due to the removal of residual stress through grinding and polishing. Influence on time-to-failure is addressed for the case with and without residual stress present. Titanium silicate glass otherwise known as ultra-low expansion (ULE)* glass is a candidate for use in applications requiring low thermal expansion characteristics such as telescope mirrors. The Hubble Space Telescope s primary mirror was manufactured from ULE glass. ULE contains 7.5% titanium dioxide which in combination with silica results in a homogenous glass with a linear expansion coefficient near zero. delayed failure . This previous study was based on a 230/270 grit surface. The grinding and polishing process reduces the surface flaw size and subsurface damage, and relieves residual stress by removing the material with successively smaller grinding media. This results in an increase in strength of the optic during the grinding and polishing sequence. Thus, a second study was undertaken using samples with a surface finish typically achieved for mirror elements, to observe the effects of surface finishing on the time-to-failure predictions. An allowable stress can be calculated for this material based upon modulus of rupture data; however, this does not take into account the problem of delayed failure, most likely due to stress corrosion, which can significantly shorten lifetime. Fortunately, a theory based on fracture mechanics has been developed enabling lifetime predictions to be made for brittle materials susceptible to delayed failure. Knowledge of the factors governing the rate of subcritical flaw growth in a given environment enables the development of relations between lifetime, applied stress and failure probability for the material under study. Dynamic fatigue is one method of obtaining the necessary information to develop these relationships. In this study, the dynamic fatigue method was used to construct a time-to-failure diagram for polished ULE glass.

Tucker, Dennis S.↗
DOE OSTI2025

Effects of HCP/BCC element ratios on the room-temperature tensile properties of Ti-Zr-Hf-Nb-Ta refractory high-entropy alloys

Equiatomic and non-equiatomic Ti-Zr-Hf-Nb-Ta refractory high-entropy alloys (RHEAs) were arc melted, homogenized, cold rolled, and recrystallized to produce single-phase, body-centered cubic (BCC), microstructures with weak texture and equiaxed grains 76–199 μm in size. Here, the non-equiatomic alloys had either a 60:40 or 80:20 atomic ratio of hexagonal close-packed (HCP) elements (Ti + Zr + Hf) to BCC elements (Nb + Ta). Alloy compositions were measured after thermomechanical processing to determine the concentrations of the major (substitutional) and minor (interstitial) elements. We investigated how elastic constants and uniaxial tensile properties were affected by changes in the relative concentrations of the constituent elements at fixed HCP:BCC ratios. Yield strengths ranged from 801 to 922 MPa and ultimate tensile strengths from 815 to 933 MPa. Good agreement is obtained between the experimental yield strengths and those predicted by a strength theory based on edge dislocations indicating that the observed compositional effects are due to their effects on shear modulus and volume misfit. Fracture occurred by dimpled rupture with fracture strains of 19.4%–25.7%, but uniform strains were an order of magnitude lower at 1.1%–3.2%, calling into question the useable ductility (prior to necking) of RHEAs considered to be ductile based on their fracture strain. Contrary to predictions in the literature that HCP elements promote ductility, our present results show that increasing the HCP:BCC ratio decreases both the total strain and the uniform strain. Similar trends were not evident in the yield or ultimate strengths; rather, strengths were affected mainly by shear modulus and volume misfit.

BCC high-entropy alloys↗
DOE OSTI2021

Performance evaluation of a Terry GS-2 steam impulse turbine with air-water mixtures

Terry steam turbines are widely used in various industries because of their robust design. Within the nuclear power generation industry, they are used in the Reactor Core Isolation Cooling System to remove decay heat during reactor isolation events. During the Fukushima Daiichi nuclear power station disaster in Japan in 2011, the Reactor Core Isolation Cooling System and associated Terry turbine operated for over 70 hours in Unit 2; this runtime is well beyond the expected operating duration. Theories suggest the turbine was subjected to a two-phase inlet flow, which could degrade the turbine performance. In this work, an experimental test rig was constructed to test a full-scale Terry model GS-2 steam turbine under two-phase air/water flows. Steady-state efficiency and torque performance maps of the turbine were developed over a range of turbine inlet pressures (1.38–4.83 bar or 20–70 psia), air mass fractions (0.05–1.0) and rotational speeds up to 4000 RPM. Furthermore, turbine performance followed expected trends with torque varying linearly and efficiency varying quadratically with rotational speed. In addition, high-speed images of the two-phase flow entering the turbine were also analyzed to understand how changes in inlet pressure and air mass fraction affect the flow regime and homogenization. The present tests with air–water two-phase mixtures are an important step towards providing an understanding of the full-scale Terry turbine’s behavior and performance curves under two-phase conditions. The results of this work will be combined with air/water and steam/water data gathered using a small-scale Terry ZS-1 steam turbine in order to understand the scaling relationship between large and small size Terry turbines and fluid pairs. The combined data set will enable further development of analytical models over a wide range of conditions and may be used to provide technical justification for expanded use of the Terry turbines in nuclear power plant safety systems and other systems.

42 ENGINEERING↗
DOE OSTI2021

Efficient Iridium Catalysts for Formic Acid Dehydrogenation: Investigating the Electronic Effect on the Elementary β-Hydride Elimination and Hydrogen Formation Steps

We report herein a series of Cp*Ir complexes containing a rigid 8-aminoquinolinesulfonamide moiety as highly efficient catalysts for the dehydrogenation of formic acid (FA). The complex [Cp*Ir(L)Cl] (HL = N-(quinolin-8-yl)benzenesulfonamide) displayed a high turnover frequency (TOF) of 2.97 × 10 4 h –1 and a good stability (>100 h) at 60 °C. Comparative studies of [Cp*Ir(L)Cl] with the rigid ligand and [Cp*Ir(L')Cl] (HL' = N-propylpypridine-2-sulfonamide) without the rigid aminoquinoline moiety demonstrated that the 8-aminoquinoline moiety could dramatically enhance the stability of the catalyst. The electron-donating ability of the N,N'-chelating ligand was tuned by functionalizing the phenyl group of the L ligand with OMe, Cl, and CF 3 to have a systematical perturbation of the electronic structure of [Cp*Ir(L)Cl]. Experimental kinetic studies and density functional theory (DFT) calculations on this series of Cp*Ir complexes revealed that (i) the electron-donating groups enhance the hydrogen formation step while slowing down the β-hydride elimination and (ii) the electron-withdrawing groups display the opposite effect on these reaction steps, which in turn leads to lower optimum pH for catalytic activity compared to the electron-donating groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A description of structured waves in shock compressed particulate composites

Dynamic compression of composite materials is of scientific interest because the mechanical mismatch between internal phases challenges continuum theories. Typical assumptions about steady wave propagation and quasi-instantaneous state changes require reexamination along with the need for time-dependent models. To that end, data and models are presented here for the shock compression of an idealized particulate composite. To serve as a generic representative of this material class, a polymer matrix was filled with tungsten particles, ranging from 1 to 50 vol. %. This creates a simple microstructure containing randomly scattered particles with an extreme impedance mismatch to the binding matrix. These materials were parallel plate impact loaded by Al flyers traveling at 1.8–5.0 km/s. Velocimetry provided records of the equilibrium state and the compression wave structure for each case with trends quantified by an empirical fit. The same quantities were also studied as a function of the wave's propagation distance. A homogenized viscoelastic model then made it possible to progress from cataloging trends to making predictions. Starting from a Mie–Gruneisen equation of state, additional time varying terms were added to capture the transient response. After calibration, accurate predictions of the steady wave structure were possible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Kelvin–Helmholtz instability under stabilizing parallel magnetic field in nonhomogeneous compressible MHD flows

We study the Kelvin–Helmholtz instability (KHI) for the general case of a compressible, nonhomogeneous, magnetized plasma flow. The study is limited to a vortex sheet interface with an imposed parallel magnetic field. We introduce a new formalism based on a convective Mach number M c , a convective Alfvénic Mach number M Ac , and a total convective Mach number that combines the two. We derive an analytic expression of the KHI growth rate for a homogeneous flow (i.e., zero Atwood number, A=0) that converges toward both the expression for unmagnetized compressible flow and Chandrasekhar's expression for magnetized incompressible flow. Otherwise, the dispersion relation is solved numerically and allows deriving general stability diagrams of magnetized KHI for the triplet (A, M c , β −plasma) parameters. We show these parameters uniquely define all configurations for a parallel magnetic field. We also construct diagrams with respect to the convective Alfvénic Mach number, the β − plasma parameter, or the magnetic field showing which magnetic field strength is required for stabilizing a given shear flow. The theoretical growth rates are compared with 18 simulations made with the GAMERA code, currently used for 3D magnetospheric simulations. Finally, we apply our results to the analysis of a past KHI experiment performed at the OMEGA laser facility, showing linear theory succeeds to provide accurate estimates of the growth rate at early times. We further discuss how our results can inform future experiments in the high-Mach magnetized regime at the National Ignition Facility. Possible limitations of the study due to resistive, mixing, or turbulence effects are discussed.

compressible flows↗
NASA NTRS1985

Stellar evolution at high mass with convective core overshooting

The transition from stellar evolution models with no convective core overshooting (CCO) at all to models in which homogeneous mixing due to CCO reaches far beyond the formal convective core boundary is systematically explored. Overshooting is parameterized in terms of the ratio d/H(p), where d is the distance of convective overshoot beyond the formal convective core boundary and H(p) is the local pressure scale height. It is concluded that CCO in very massive main sequence stars produces a great expansion of the stellar envelope if d/H(p) is large but not excessively large. CCO does not entirely suppress convective instability above the overshoot zone in the envelopes of main sequence stars more massive than about 15 solar masses. A general comparison of theoretically constructed isochrones for young stars with observed main sequence turnups indicates that the observed turnups are longer, brighter, and cooler at the tip than those expected on thfe basis of standard evolutionary theory.

Stothers, R. B.↗
NASA NTRS2017

Scale Dependence of Multiplier Distributions for Particle Concentration, Enstrophy, and Dissipation in the Inertial Range of Homogeneous Turbulence

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

turbulent flows↗
NASA NTRS1950

Isentropic phase changes in dissociating gases and the method of sound dispersion for the investigation of homogeneous gas reactions with very high speed : Conclusion

The analytical results of Part I are also applied to sound dispersion by friction and heat conduction, An irreversible change of momentum, energy, and type of particle corresponding to friction, heat conduction, and diffusion effects can appear both in the direction of the sound field and traverse to it. Longitudinal damping, the coupling of longitudinal damping and that due to chemical and physical changes, and coupling of diffusion and compositional changes are treated for a plane sound wave of infinite extent. The same principles are also applied to sound effects in cylindrical tubes. The limitations of the method are discussed in some detail.

SOUND VELOCITY - GASES↗
NASA NTRS1986

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗
DOE OSTI2024

Theoretical Investigation of the Hydrogenation of Cyclohexene Catalyzed by Supported Single-Atom Sites on Redox Noninnocent LiMn 2 O 4 and Li 2 Mn 2 O 4 Surfaces

Here, the tuning of catalyst activity via stereoelectronic modulation of the active-site structure remains a grand challenge in heterogeneous catalysis. In homogeneous catalysis, the redox noninnocent ligands can be introduced to organometallic fragments to donate electrons to the metal center and fine-tune the catalytic activity. Analogously, lithium-ion battery materials, such as lithium manganese oxide (LMO), lithium titanium oxides (LTO), etc., can serve as redox noninnocent catalyst support to modulate the electronic structures of the active site via lithiation, hence tuning the catalytic activity of supported active sites. Experimentally, the Ni single-atom site was supported on LiMn 2 O 4 via oxidative grafting and exhibited no catalytic activity toward the hydrogenation of cyclohexene. After introducing additional Li into the catalyst support forming Li 2 Mn 2 O 4 , the Ni single-atom site becomes active, with the catalytic rates increasing as a function of the lithiation for Li/Mn ratios >0.9. In this paper, density functional theory (DFT) calculations are performed to study the Ni site structure via X-ray absorption near edge structure (XANES) simulations and investigate the electronic properties of Ni single-atom site before and after the addition of intercalated lithium in the LMO spinel structure. Furthermore, the study of the reaction mechanism is also carried out to understand the thermodynamically and kinetically favored pathways. XANES simulation suggests that the Ni single-atom site is likely to stay in the Li channel of the spinel support structure and form an octahedral structure. After Li intercalation, the Ni site becomes less positively charged, indicating the partial reduction of the Ni site. The simulated reaction energy profile over the LiMn 2 O 4 support exhibits high-energy barriers (1.07 eV) for the hydrogenation of cyclohexene; however, the Li 2 Mn 2 O 4 support is able to better stabilize low-coordinated ion sites and improve ion mobility, leading to lower overall energy barriers (0.64 eV). The reduced and low-coordinated ion site, thus, can better stabilize the reaction intermediates and promote hydrogenation reaction. Similarly, other transition metal ions (Fe, Co, and Cu) are also considered over the LiMn 2 O 4 and Li 2 Mn 2 O 4 catalyst supports for hydrogenation reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Miscibility and Cocrystallization in Ethylene–Vinyl Alcohol Copolymer Blends

The compatibility among different ethylene−vinyl alcohol (EVOH) copolymer grades plays a crucial role in determining how easily they can be recycled when present together in a mixed waste stream. In this work, melt miscibility and cocrystallization in 50/50 wt/wt binary blends of EVOH copolymers with differing ethylene content were studied. Blends with up to a 21 mol % difference in composition were analyzed. Thin films of miscible blends appeared homogeneous in the melt as observed under an optical microscope, whereas AFM height images showed that immiscible blends underwent surface roughening due to phase separation. For copolymers with modest composition differences, the blend behaved as a single component, showing single, narrow melting and crystallization peaks in DSC thermograms, indicating cocrystallization at the level of crystal stems. Interestingly, even phase-separated blends demonstrated partial cocrystallization due to partial miscibility of the components in the molten phase-separated domains. The extent of cocrystallization is governed by the difference in freezing points of the components; rapid cooling increased cocrystallization in the blends. The maximum compositional difference allowed for miscibility is not constant but depends on the blend’s average comonomer content, in agreement with the “miscibility window” calculated from literature pressure−volume−temperature behavior for the individual EVOH copolymers and regular mixing theory. This study helps illuminate the effect of copolymer composition on miscibility, as well as cocrystallization behavior in blends of random copolymers with cocrystallizable units.

Cocrystallization↗
DOE OSTI2022

A micromorphic filter for determining stress and deformation measures from direct numerical simulations of lower length scale behavior

A micromorphic filter is presented for the extraction of stress and deformation measures from underlying direct numerical simulation (DNS) of microstructural mechanical response. The filter is consistent with the micromorphic continuum theory of Eringen and Suhubi (1964), and allows the interrogation of a DNS to generate higher order constitutive models. The filter adopts aspects of the overlap coupling techniques for atomistic-continuum scale-bridging in order to update the nodal degrees of freedom of the finite-element-based filter. Here, two methods for the extraction of quantities of interest from the underlying DNS are presented. The first is a least squares fitting technique which is appropriate for finite-element-style macro-scale domains, and the second is a variationally based approach which generalizes the method to any macro-scale domain which has a variational form. No restrictions on the form of the micro-scale simulation are inherent to the approach, provided that the required quantities (stress, position, etc.) can be provided. The filter is applied to a simple homogeneous medium undergoing homogeneous deformation to demonstrate the recovery of a classical continuum response, what we call the null case. We then apply the framework to the same homogeneous medium with a central and edge penny-shaped crack to show micromorphic effects. We demonstrate that varying the size of the filter causes the micromorphic behaviors to arise and then dissipate as the filter becomes smaller than the crack's length scale. Additionally we show the effect of filter size on a chiral element network along with a plate perforated with evenly spaced and perturbed holes through the thickness. The micromorphic effects are shown to be present for the chiral elements under any loading but become most pronounced when a single element is located within each averaging domain. Micromorphic effects become pronounced for the plate upon the onset of localization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On hydromagnetic wave interactions in collisionless, high- β plasmas

We describe the interaction of parallel-propagating Alfvén waves with ion-acoustic waves and other Alfvén waves, in magnetized, high- β collisionless plasmas. This is accomplished through a combination of analytical theory and numerical fluid simulations of the Chew–Goldberger–Low (CGL) magnetohydrodynamic (MHD) equations closed by Landau-fluid heat fluxes. An asymptotic ordering is employed to simplify the CGL-MHD equations and derive solutions for the deformation of an Alfvén wave that results from its interaction with the pressure anisotropy generated either by an ion-acoustic wave or another, larger-amplitude Alfvén wave. The difference in time scales of acoustic and Alfvénic fluctuations at high- β means that interactions that are local in wavenumber space yield little modification to either mode within the time it takes the acoustic wave to Landau damp away. Instead, order-unity changes in the amplitude of Alfvénic fluctuations can result after interacting with frequency-matched acoustic waves. Additionally, we show that the propagation speed of an Alfvén-wave packet in an otherwise homogeneous background is a function of its self-generated pressure anisotropy. This allows for the eventual interaction of separate co-propagating Alfvén-wave packets of differing amplitudes. The results of the CGL-MHD simulations agree well with these predictions, suggesting that theoretical models relying on the interaction of these modes should be reconsidered in certain astrophysical environments. Applications of these results to weak Alfvénic turbulence and to the interaction between the compressive and Alfvénic cascades in strong, collisionless turbulence are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Renormalized site density functional theory

Site density functional theory (SDFT) provides a rigorous framework for statistical mechanics analysis of inhomogeneous molecular liquids. The key defining feature of these systems is the presence of two very distinct interactions scales (intra- and inter-molecular), and as such proper description of both effects is critical to the accuracy of the calculations. Current SDFT applications utilize the same approximation scheme for both interaction motifs, which negatively impacts the results. Dual space methodology, used in this work, alleviates this issue by providing the flexibility of evaluating part of the interactions in traditional field representation. For molecular liquid this translates into retaining density representation for inter-molecular interactions but describing stiff intra-molecular remainder by more appropriate conventional field based methods. This opens the way to decouple analysis of the two interactions scales - the idea which is developed further in this work for the case of homogeneous reference approximation of inter-molecular interactions. We demonstrate that by defining new collective variables, the behavior of the original molecular liquid system at the inter-molecular level can be transformed to resemble that of an effective simple fluid mixture. The latter is linked to intra-molecular scale through renormalized interaction parameters. We illustrate this renormalization procedure for several types of diatomic liquids, showing that this approach cures many of the shortcomings of existing SDFT methods.

Chuev, Gennady N.↗
NASA NTRS1978

Numerical solutions and laser-Doppler measurements of spin-up

The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. A series of laser-Doppler measurements was made of the zonal flow over a range of Ekman numbers and Rossby numbers at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.

Warn-Varnas, A.↗